The Dems should absolutely do this. But they'll probably hem and haw about norms.

The way Tuberville did this is a little esoteric. Unlike the House, the Senate gives a lot of privileges to a single Senator. Rand Paul is notorious for being a douche in this regard.

So a lot of Senate business is done by unanimous consent to speed things up and avoid traditional procedure. As you'd figure, it requires all senators to approve.

For military nominations/promotions, the Senate traditionally does them in bulk by unanimous consent, rather than holding individual floor votes on each person.

If one Senator objects, the Senate can proceed to an individual vote on each nominee and just invoke cloture and bypass the Senator.

In the case of nominations/promotions, they have only needed 50 votes instead of the usual 60 to invoke cloture since 2013. But individual floor votes on each nomination take a lot of time to do. The military alone has hundreds of positions that need to be filled.

Holding individual votes and invoking cloture on all those nominations would mean the Senate would basically only be doing that all session.

So that's how Tuberville held up military promotions for so long.